X2-200x+9200=0

Solution for X2-200x+9200=0 equation:

X2-200X+9200=0

We add all the numbers together, and all the variables

X^2-200X+9200=0

a = 1; b = -200; c = +9200;
Δ = b2-4ac
Δ = -2002-4·1·9200
Δ = 3200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-40\sqrt{2}}{2*1}=\frac{200-40\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+40\sqrt{2}}{2*1}=\frac{200+40\sqrt{2}}{2}
$